Bottom Line:
The largest outbreak of Ebola to date is currently underway in West Africa, with 3944 cases reported as of 5th September 2014.Our analysis suggests that the person-to-person reproduction number was 1.34 (95% CI: 0.92-2.11) in the early part of the outbreak.Using stochastic simulations we demonstrate that the same epidemiological conditions that were present in 1976 could have generated a large outbreak purely by chance.

Affiliation: Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, United Kingdom. Electronic address: anton.camacho@lshtm.ac.uk.

fig0010: Schematic of model structure. Individuals start off susceptible to infection (S). Upon infection they enter an incubation period (E), then at symptom onset they become infectious in the community (I). After this point, they either: enter a recovered state (R); remain infectious and go into hospital (H); or die and remain infectious (D) until buried (B). Hospitalised infectives also move either into the recovered or dead compartment. Finally, the E compartment is split according to the route of transmission in order to keep track whether a case was infected via contaminated syringes at the hospital (Eh) or by person-to-person contact (Epp) with either an infective in the community or a dead but not buried case. The forces of infection for the two transmission processes are λh(t) = βh(t)H/N and λpp(t) = (βi(t)I + βd(t)D)/N, where βh(t), βi(t) and βd(t) are the time-varying transmission rates given by Eq. (1). Other parameters are as follows: ϵ, inverse of the mean incubation period; γh, γd and γr, inverse of the mean duration from symptom onset to hospitalization, death and recovery respectively; νd and νr, inverse of the mean duration from hospitalization to death and recovery respectively (see Eq. (7)); μb, inverse of the mean duration from death to burial; κi(t) is computed to ensure that the overall hospitalisation rate is equal to κ until hospital closure (see Eq. (5)); ϕi and ϕh are computed to ensure that the overall case–fatality ratio is equal to ϕ (see Eq. (4)). Parameter values and prior assumptions can be found in Table 2. The model was simulated by integrating the set (3) of ordinary differential equations using the SSM library (Dureau et al., 2013).

Mentions:
We used a compartmental model of infection to analyse the temporal dynamics of Ebola (Legrand et al., 2007). The model structure is outlined in Fig. 2. We assumed that individuals start off susceptible to infection (S). Upon infection they enter an incubation period (E), then become symptomatic and infectious in the community (I). We therefore assume that the latent and incubation periods are equivalent. After this point, they either: enter a recovered state (R); remain infectious and go into hospital (H); or die and remain infectious (D) until buried (B). Following hospitalisation, infectious hosts also move either into the recovered or dead compartment.

fig0010: Schematic of model structure. Individuals start off susceptible to infection (S). Upon infection they enter an incubation period (E), then at symptom onset they become infectious in the community (I). After this point, they either: enter a recovered state (R); remain infectious and go into hospital (H); or die and remain infectious (D) until buried (B). Hospitalised infectives also move either into the recovered or dead compartment. Finally, the E compartment is split according to the route of transmission in order to keep track whether a case was infected via contaminated syringes at the hospital (Eh) or by person-to-person contact (Epp) with either an infective in the community or a dead but not buried case. The forces of infection for the two transmission processes are λh(t) = βh(t)H/N and λpp(t) = (βi(t)I + βd(t)D)/N, where βh(t), βi(t) and βd(t) are the time-varying transmission rates given by Eq. (1). Other parameters are as follows: ϵ, inverse of the mean incubation period; γh, γd and γr, inverse of the mean duration from symptom onset to hospitalization, death and recovery respectively; νd and νr, inverse of the mean duration from hospitalization to death and recovery respectively (see Eq. (7)); μb, inverse of the mean duration from death to burial; κi(t) is computed to ensure that the overall hospitalisation rate is equal to κ until hospital closure (see Eq. (5)); ϕi and ϕh are computed to ensure that the overall case–fatality ratio is equal to ϕ (see Eq. (4)). Parameter values and prior assumptions can be found in Table 2. The model was simulated by integrating the set (3) of ordinary differential equations using the SSM library (Dureau et al., 2013).

Mentions:
We used a compartmental model of infection to analyse the temporal dynamics of Ebola (Legrand et al., 2007). The model structure is outlined in Fig. 2. We assumed that individuals start off susceptible to infection (S). Upon infection they enter an incubation period (E), then become symptomatic and infectious in the community (I). We therefore assume that the latent and incubation periods are equivalent. After this point, they either: enter a recovered state (R); remain infectious and go into hospital (H); or die and remain infectious (D) until buried (B). Following hospitalisation, infectious hosts also move either into the recovered or dead compartment.

Bottom Line:
The largest outbreak of Ebola to date is currently underway in West Africa, with 3944 cases reported as of 5th September 2014.Our analysis suggests that the person-to-person reproduction number was 1.34 (95% CI: 0.92-2.11) in the early part of the outbreak.Using stochastic simulations we demonstrate that the same epidemiological conditions that were present in 1976 could have generated a large outbreak purely by chance.

Affiliation:
Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, United Kingdom. Electronic address: anton.camacho@lshtm.ac.uk.